A geometric classification of some solvable groups of homeomorphisms
Abstract
We investigate subgroups of the group PLo(I) of piecewise-linear, orientation-preserving homeomorphisms of the unit interval with finitely many breaks in slope, under the operation of composition, and also subgroups of the generalized Thompson groups F_n. We find geometric criteria determining the derived length of any such group, and use this criteria to produce a geometric classification of the solvable and non-solvable subgroups of PLo(I) and of the F_n. We also show that any standard restricted wreath product C wr T (of non-trivial groups) that embeds in PLo(I) or F_n must have T isomorphic with the integers.
Keywords
Cite
@article{arxiv.math/0602036,
title = {A geometric classification of some solvable groups of homeomorphisms},
author = {Collin Bleak},
journal= {arXiv preprint arXiv:math/0602036},
year = {2014}
}
Comments
19 pages, in preparation. Portions of this paper contain portions of the author's dissertation written at Binghamton University. Newer versions contain improved grammar, corrected typos and minor re-arrangements